By utilizing the concepts and methods developed in Algebra Topology, Algebra Geometry and Algebra Representations, we first depicted the concepts and results of Incidence Algebra which reflects the linear structure of underlying posets and Sheaf theory which reflects the topological structure of underlying poset in the framework of Category Theory.
本文综合运用了代数拓扑、代数几何及代数表示论里发展起来的概念与方法，首先在范畴的框架下，对和偏序集的线性结构密切相关的Incidence代数，及与偏序集的拓扑结构紧密联系的层，进行了刻画。
The theory of graphs and relations between the spectra and fixed variate (e. g. chromatic number, degree sequence, diameter and connectivity) of graphs by means of the well-developed theory and technique of algebra, topological structure properties of graph, combination and matrix theories so as to establish firm essential relation between the algebraic properties and topological properties of graphs and networks.
图谱理论的研究主要是利用成熟的代数理论和技巧，并结合图的拓扑结构性质和组合数学的理论、矩阵理论来研究图谱及其与图的结构性质、图的其它不变量(如色数，度序列，直径，连通度等)之间的关系，将图与网络的代数性质与图的拓扑性质紧密地联系在—起。
A topological space based on LI-ideals of a lattice implication algebra is constructed, and its topological properties, such as separability, compactness and connectedness are discussed.
将格蕴涵代数中全体LI-理想构成一个拓扑空间，并讨论了其拓扑性质，如可分离性、紧致性和连通性等。
In this paper, from the six-term exact sequence, it is proved that the direct sum of Z and K1 - group of a Toeplitz algebra is always isomorphic to the topological K1 - group of the boundary of the relative domain.
本文通过六项正合列计算出，在强拟凸域上，它的拓扑边界上连续函数代数的K（1-）群同构于区域上Toeplitz代数的K1-群与Z的直和。
Further more, we prove that the cohomotopy groups is isomorphic to K1 -group of the continuous algebra on topological boundary of bounded domains in C.
进一步证明了：在复平面C中，任意有界域的拓扑边界上连续函数代数的K_1-群与其边界上的上同伦群同构。
Finding the Tree-Set of Linear Graph by the Method of Topological Tree-Group of the Field Mod 2 Algebra
求线图树集的综合方法&二模域代数拓扑树组法
At last, based on the data structure of AVL used for moving objects, spatio-temporal topological analysis algorithms are specified, which makes the use of the concept of Realms and ROSE algebra and is implemented by integrating Plane Sweep algorithm with the factor of time interval.
最后基于Realms概念和ROSE代数，根据时空数据库中移动空间对象存储的平衡二叉树的数据结构，用平面扫描算法结合时间域的方法实现了具体的时空拓扑分析算法，并进行了时间复杂性讨论。
Having analysed the " W-algebra ", " K-tree terms " and " MINTY ", the three typical methods of generating direct tree terms, the paper advances a new topological one.
本文在对王氏代数、k-树组和MINTY这三种求有向树组的典型方法进行分析之后，提出了一种生成有向树组的拓扑方法。
The Topological Molecular Lattic over~EI Algebra and Its Application to Cluster Analysis
~EI代数上的拓扑分子格及其在聚类分析中的应用
To study the topological structure of the AFS structures, in this paper, the investigation of properties and structures of EI n algebra and EI n algebra is continued.
为了讨论AFS.结构的拓扑性质，本文在[1]、[2]的基础上，进一步讨论了EIn代数和EIn代数的性质与结构。
It is widely considered that mathematical parent structures include algebra structure, sequence structure and topological structure. Compared the actuality of the structure of th Using AFS algebra and AFS structure, any human ordinary fuzzy concept can be represented.
数学母结构通常说只有代数结构、序结构和拓扑结构；
Moreover, they prove that the set S (D) of all subsystems of a topological system D is a complete Heyting algebra.
最后证明了一个拓扑系统D的全部子系统所构成的集合S（D）在包含序下是一个完备的Heyting代数。
And prove that the cohomotopy groups is isomorphic to K_1-group of the continuous algebra on topological boundary of domains in C.
并进一步证明了在复平面C上，任意区域的拓扑边界上的连续函数代数的K1群与它边界上的同伦群同构。
Based on the outcome of Xu Yang and Qin Keyun about lattice implication algebra and lattice-valued prepositional logic LP with truth-value in a lattice implication algebra, the author studied the properties of lattice implication algebra and the α-automated reasoning method based on α-resolution principle of LP. The specific contents are as follows: The Study of Lattice Implication Algebra On the basis of previous results of lattice implication algebra, this part consists of the following three points: 1. Some properties of lattice implication algebra L were discussed, and some important results were given if L was a complete lattice implication algebra. 2. The properties of left idempotent elements of lattice implication algebras were discussed, and the conclusion that lattice implication algebra L was equals of the directed sum of the range and dual kernel of a left map constructed by a left idempotent element was proved. 3. The properties of the filters of lattice implication algebra were discussed, the theorem was shown that they satisfy the hypothetical syllogism and substitute theorem of the propositional logic. 4. The concept of weak niters of lattice implication algebras and their properties and structures are discussed. It is proved that all weak filters of a lattice implication algebra form a topology and the the implication isomorphism betweem two lattice implication algebras is a topological mapping between their topological spaces. The Study of α-automated reasoning method based on the lattice-valued propositional logic LP In this part, the author given an a-automated reasoning method based on the lattice-valued propositional logic LP.
本文基于徐扬和秦克云的关于格蕴涵代数和以格蕴涵代数为真值域的格值命题逻辑系统LP的研究工作，对格蕴涵代数以及格值命题逻辑系统LP中基于α-归结原理的自动推理方法进行了系统深入的研究，主要有以下两方面的研究成果：一、关于格蕴涵代数的研究 1、对格蕴涵代数的格论性质进行了研究，得到了当L为完备格蕴涵代数时，关于∨，∧，→运算的一些结果； 2、对格蕴涵代数的左幂等元进行了研究，证明了格蕴涵代数L可以分解为任何一个左幂等元所对应的左映射的像集合与其对偶核的直和； 3、对格蕴涵代数的滤子的性质进行了研究，证明了滤子的结构相似于逻辑学中的Hypothetical syllogism规则和替换定理； 4、给出了格蕴涵代数中弱滤子的概念，对弱滤子的性质个结构进行了研究，证明了格蕴涵代数的全体弱滤子构成一个拓扑结构，格蕴涵代数之间的蕴涵同构是相应的拓扑空间之间的拓扑映射。